Here are changes that some mutual-fund managers believe are crucial for another big climb in stocks

Whether they are bullish or bearish on Japanese stocks, mutual-fund managers generally agree it will be an uphill battle for the country to achieve the kind of fundamental economic and corporate changes that would fuel a long-term market rally.

Fund managers say a sustained rally depends on factors including wage increases in Japan that would help spur the economy, a further weakening of the yen to stimulate exports and boost...